T. Iliescu, "Genuinely Nonlinear Models for Convection-Dominated Problems," Preprint ANL/MCS-P857-1100, November 2000. [pdf]
This paper introduces a general, nonlinear subgrid-scale (SGS) model, having bounded artificial viscosity, for the numerical simulation of convection-dominated problems. We also present a numerical comparison (error analysis and numerical experiments) between this model and the most common SGS model of Smagorinsky, which uses a p-Laplacian regularization. The numerical experiments for the 2-D convection-dominated convection-diffusion test problem show a clear improvement in solution quality for the new SGS model. This improvement is consistent with the bounded amount of artificial viscosity introduced by the new SGS model in the sharp transition regions.